The raw material in making music are sounds. While the term sound covers a host of characteristics, in this application the particular characteristic of the sounds which are produced, which is varied or controlled is the frequency. Thus, when sound is used herein the characteristic that is controlled or selected is its frequency. Man can in general hear sounds with frequency range between 15 and 24,000 hertz, the frequency of sounds which musicians use lie in the smaller range of about 20 to 10,000 hertz. Occasionally other sounds are used in music, for example certain huge organs can produce sounds with frequencies in the vicinity of 16,000 hertz. However, while humans can hear sounds within the large range mentioned above, they cannot distinguish between two sounds when their frequencies are too close together. The arrangement of sounds in the ascending order of their frequencies which can be separately distinguished is a set of different sounds which comes to a total of about 2,000. In Occidental music, musicians use a much smaller number of sounds, for example 110 sounds in the range 21.8 hertz to 10,548 hertz, where each sound or tone has a frequency with a ratio of 1.06 to the next adjacent lower tone or sound. Sounds whose frequencies have the ratio 1:2.sup.n (where n is an integer) have so many identical characteristics that they are sometimes referred to as the "same" sound.
Sounds with this frequency ratio are usually separated by an interval of 12 different sounds in the set of 110 sounds mentioned above. For this reason, we commonly refer to the entire set of 110 different sounds as if there are only 12, using only 12 different names over and over again.
Thus, in Occidental music as well as music of other cultures, there is a reduction of the available raw material employed which is connected with the election of a given set of sounds. For purposes of description, we will call such smaller sets of sounds which musicians specially choose to use, Politones; and the sounds which belong to them are tones.
Examples of different Politones are the Great Perfect Systems and the Lesser Perfect Systems of ancient Greek music, the Equal Temperament, the Pure or Just Temperament and the Mean Tone Temperaments of Occidental music, etc. Since the reduction of the available raw material to a given Politone is not arbitrary, but well grounded in underlying acoustical relationships among its tones, the specific reduction is, to a great extent, responsible for the principle characteristics and development of the music which uses that particular Politone.
Some instruments, like the human voice, violas, violins, etc., are readily capable of playing music in any given Politone because they are able to produce a continuous set of sounds. Other instruments, for example the piano, harp and Kithara, can be tuned to produce the tones of different Politones. Still other instruments, like flutes, horns, etc., are much less flexible and are generally made to produce the tones of a given Politone.
Even with the most flexible of instruments, it is difficult to play in Politones of different cultures when these Politones have a larger number of tones spaced at smaller intervals. In such cases, it is not easy to recognize such small intervals by ear, and accordingly to find those tones in continuous instruments. Sometimes it is necessary to use an acoustical device to tune an instrument, like the harp, to give tones of a desired Politone. Once a Politone is familiar to use, we can sing it or play it on continuous instruments. Similarly, it is difficult to play music in Politones used a long time ago even in our own culture (the irregular tunings used during the 18th century or the various shades of Mean Tone temperament, etc.). For this reason, accurate examples of music of different cultures and epochs are generally not available to the public at large or even students of music. Sometimes a composer who wants to experiment with a new Politone may have to build up a novel instrument for that Politone itself.
As a result of the relatively new capability of synthesizing sounds by electronic means, it is now possible to produce sounds of any desired pitch (frequency). However, notwithstanding this significant flexibility, electronic musical instruments still use the traditional keyboard with its configuration of black and white keys which is related to the use of a particular Politone (i.e. the Equal Temperament) and some others which are very similar to it. For example, when teachers and composers want to use a Politone containing 32 tones equally spaced within each octave, each octave is spanned by 32 traditional keys, which is rather inconvenient because the number of octaves that the keyboard can accommodate is then severely reduced. Also the particular configuration of white and black keys is, in this case, not only of no use, but is actually a hindrance. Likewise, when the intervals between the tones are not equal, there is no way of visually displaying that difference on the keyboard. Even in the equal tempered system, the traditional keyboard does not display the intervals between different sounds. An additional constraint of the traditional keyboard is the inability to produce portamento and vibrato which are cherished techniques of musical expression.
In Occidental music, there is usually a further reduction in the raw material of sounds employed which is connected with the election of a given tonality. The election of a given tonality by a composer is an indication to a predisposition to give a particular sound, which is called a tonic, a conspicuous role in the piece by means of using mostly a subset of sounds which are in deep connection with a tonic. With such a subset, it is possible to emphasize, reinforce, announce or simply suggest the presence of the tonic.
A scale is the arrangement, in ascending order of frequencies, of the tonic along with the subset of sounds which are in deep connection with the tonic. Since tonalities can be major or minor (major tonalities are described as affirmative and optimistic, minor tonalities as inquisitive and melancholy) there are major and minor scales. Any major scale for instance has seven sounds, the role names of these sounds and the size of intervals between them are shown in FIG. 12. Since 12 different sounds can be taken as a tonic we therefore have 12 different major scales. As shown in FIG. 13, the election of a given tonality produces a division of the whole set of sounds into two subsets, the subset of those that belong to the scale that is being used and the subset of sounds that do not belong. This division does not mean that the election of a given tonality excludes the use of sounds outside the given scale, for with them it is possible to hide, camouflage, evade or make dissonant the presence of the tonic.
The nomenclature of sounds in traditional notation is based on the division which the election of the C major tonality imposes on the set of sounds. Traditional notation has a first class of names for the seven sounds which belong to the C major scale: in particular C, D, E, F, G, A and B; and a second class of names for the five sounds outside the C major scale (each of these sounds has two different names), e.g., C sharp--D flat, D sharp--E flat, F sharp--G flat, G sharp--A flat, A sharp--B flat. It is this same division which is imposed on the piano keyboard, the white keys correspond to the sounds of the C major scale and the black keys correspond to the sounds outside the scale.
When a major tonality is elected whose tonic is C, then it is very convenient that the 12 sounds in the octave are classified into two different groups according to their relation to the C major scale. However, this nomenclature which is so helpful and illustrative for the C major tonality is definitely obstructive for any other tonality, for it appears to suggest a division of the set of sounds that is not the one actually being used. Because the division is artificial in every case (except C major), it must constantly be rectified by using alterations (and reiterated alterations) which leads to a rather inelegant notational system creating not only several different names for the same sound but also purely notational phenomena such as the susceptibility of chords to various interpretations.
Moreover, traditional notation and traditional musical nomenclature are (not surprisingly) closely connected with the Politones that have been traditionally used in the Western culture during the last 300 years. Thus, this notation and nomenclature are also of little or no use to represent and describe structures of music which differ dramatically from the traditional ones.
I have developed a musical notation, see "Una Nueva Notacion Musical" by Skliar, et al., appearing in Editorial Episteme (Buenos Aires 1976) which provides a unity for the notation of all kinds of music and whose visual patterns are the natural counterpart of the aural patterns they represent. That notation will be briefly described here since a method of using my keyboard has important relationships to the notation. This description will start with an explanation of how to use it to notate music in equal temperament because it is the Politone most familiar to us, however it will be apparent how to use it to notate music in any desired Politone.
The notation which is described here is called Cartesian, because its basic feature is the representation of sounds in a Cartesian coordinate plane by means of their parameters of pitch (frequency) and duration. Pitch has been logarithmically represented, and both pitch and duration are represented as discrete magnitudes. (See FIG. 14). In order to notate a given composition in equal temperament, a grill work, called the poligram, like the one shown in FIG. 14 is used. The spaces between two parallel horizontal lines are called interlines. The poligram used in each case must have at least as many interlines as there are sounds spaced in semitones between (and including) the lowest and the highest sound of the composition. From bottom to top each interline belongs respectively to each one of those sounds arranged from the lowest to the highest. The correspondence between the tones of equal temperament and interlines is designated on the left side of the poligram as shown in FIG. 14. When the composition is written in a given tonality, the interlines which correspond to the sounds of the tonic chord of that tonality can be shaded, as also seen in the figure.
Each sound is represented by a trapezium (or indicium) placed in the corresponding interline. The length of the base of the trapezium shows the duration of the sound. Sounds of the smallest duration in the composition must be represented by a trapezium whose base covers the distance between two consecutive parallel vertical lines of the poligram. Sounds which are 2, 3, 4 times, etc. longer must be represented, respectively, by trapeziums whose bases extend over the distances between 2, 3, 4, etc. consecutive parallel vertical lines of the poligram. Vertical lines which correspond to the end of each measure may be highlighted in the poligram as also seen in the figure.
In the same way that the election of a given tonality is indicated by means of shading, those interlines which correspond to the sounds of the tonic chord, likewise, when a modal scale, a non-traditional tonality, or non-tonality is used, either the appropriate interlines can be shaded, or none at all. If a Politone other than equal temperament is used, as in microtonalism, or music of different cultures, the correspondence between tones and interlines is accordingly changed.
In Cartesian notation the size of intervals between the written sounds can be recognized immediately by the eye, just as the aural effect of the interval is recognized by the ear; to notate different transpositions of a given music score is as easy as it is to sing the represented music at different pitches. Finally, the notation enables any musical phenomenon to have a spatial counterpart within the poligram.
However, either with this or any other system of notation the piano keyboard, due to the artificial division between the tones associated with the C major scale, and all other tones, associates different configurations of keys with what are identical aural phenomena. Because the Equal Temperament is a regular tuning, each tone is no more or less important than any other tone. Accordingly the keyboard for playing or composing music should not suggest an artificial division between sounds, as is suggested by the piano keyboard or keyboards similar thereto.
As described in my co-pending application entitled "Linear Keyboard Adapter" filed Aug. 18, 1982, S.N. 409,250, and now abandoned a conventional piano keyboard has 88 keys, seven white keys and five black keys in each octave. Non-conventional pianos may have more or less than 88 keys, but each have the same the division of keys per octave. Other instruments (both those that produce music mechanically as well as the newer instruments which produce music electronically) may have more or less than 88 keys, but again the relationship of seven white keys and five black keys per octave is maintained. Throughout the remainder of this application, those keyboards will be referred to as a piano keyboard, regardless of whether or not the keyboard is part of a piano, so long as it has the conventional seven white keys and five black keys per octave.
Although this complement of seven white keys and five black keys per octave is traditional, there have been suggestions for alterations in this relationship. For example Coles in U.S. Pat. Nos. 3,845,685; 3,943,811; 3,973,460 and 3,986,422 suggest a keyboard which includes five white keys and at most five black keys per octave, or a total of a maximum ten keys per octave. On the other hand, other proposals (see House U.S. Pat. No. 2,097,280 and Young U.S. Pat. No. 2,706,926) suggest increasing the number of keys per octave. In the case of House, he suggests 18 keys per octave, six white keys, six long black keys and six short black keys. Young on the other hand, suggests 24 keys per octave, again using a combination of long and short keys, in three different tiers. The upper and lower tiers include seven keys, and the intermediate tier includes ten keys. Each of these keyboards is restricted to one or a few Politones, none are able to produce portamento or vibrato. All of the keyboards retain an uneven configuration of keys which has no correspondence with the intervals among the sounds which the keys produce.